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A269303 Numbers k such that (266*10^k + 1)/3 is prime.

%I A269303 #24 May 26 2024 15:49:09
%S A269303 0,1,2,3,4,5,6,8,10,13,19,26,37,69,77,81,214,242,255,900,1113,1833,
%T A269303 3166,3566,4753,4849,4869,5005,7372,7702,10240,16100,18972,28574,
%U A269303 33815,37820,70457,89482,106066,133603,154897,278325
%N A269303 Numbers k such that (266*10^k + 1)/3 is prime.
%C A269303 For k > 0, numbers k such that digits 88 followed by k-1 occurrences of digit 6 followed by the digit 7 is prime (see Example section).
%C A269303 a(43) > 3*10^5.
%H A269303 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 886w7</a>.
%e A269303 6 is in this sequence because (266*10^n+1)/3 = 88666667 is prime.
%e A269303 Initial terms and associated primes:
%e A269303 a(1)  = 0,    89;
%e A269303 a(2)  = 1,    887;
%e A269303 a(3)  = 2,    8867;
%e A269303 a(4)  = 3,    88667;
%e A269303 a(5)  = 4,    886667;
%e A269303 a(6)  = 5,    8866667;
%e A269303 a(7)  = 6,    88666667;
%e A269303 a(8)  = 8,    8866666667;
%e A269303 a(9)  = 10,   886666666667;
%e A269303 a(10) = 13,   886666666666667, etc.
%t A269303 Select[Range[0, 100000], PrimeQ[(266*10^#+1)/3] &]
%o A269303 (Magma) [n: n in [0..220] | IsPrime((266*10^n + 1) div 3)]; // _Vincenzo Librandi_, Feb 23 2016
%o A269303 (PARI) is(n)=ispseudoprime((266*10^n + 1)/3) \\ _Charles R Greathouse IV_, Feb 16 2017
%Y A269303 Cf. A056654, A268448.
%K A269303 nonn,more
%O A269303 1,3
%A A269303 _Robert Price_, Feb 22 2016
%E A269303 a(39)-a(41) from _Robert Price_, Apr 22 2020
%E A269303 a(42) from _Robert Price_, May 31 2023